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Group systems, groupoids, and moduli spaces of parabolic bundles
K. Guruprasad, J. Huebschmann, L. Jeffrey, and A. Weinstein
Source: Duke Math. J. Volume 89, Number 2
(1997), 377-412.
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Mathematical Reviews number (MathSciNet): MR1460627
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Digital Object Identifier: doi:10.1215/S0012-7094-97-08917-1
References
[1] M. Atiyah, The geometry and physics of knots, Lezioni Lincee. [Lincei Lectures], Cambridge University Press, Cambridge, 1990.
Mathematical Reviews (MathSciNet): MR92b:57008
Zentralblatt MATH: 0729.57002
[2] M. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1983), no. 1505, 523–615.
Mathematical Reviews (MathSciNet): MR85k:14006
Zentralblatt MATH: 0509.14014
Digital Object Identifier: doi:10.1098/rsta.1983.0017
JSTOR: links.jstor.org
[3] R. Bieri and B. Eckmann, Relative homology and Poincaré duality for group pairs, J. Pure Appl. Algebra 13 (1978), no. 3, 277–319.
Mathematical Reviews (MathSciNet): MR80k:20048
Zentralblatt MATH: 0392.20032
Digital Object Identifier: doi:10.1016/0022-4049(78)90012-9
[4] I. Biswas and K. Guruprasad, Principal bundles on open surfaces and invariant functions on Lie groups, Internat. J. Math. 4 (1993), no. 4, 535–544.
Mathematical Reviews (MathSciNet): MR94i:58033
Zentralblatt MATH: 0789.58017
Digital Object Identifier: doi:10.1142/S0129167X93000285
[5] I. Biswas and K. Guruprasad, On some geometric invariants associated to the space of flat connections on an open space, Canad. Math. Bull. 39 (1996), no. 2, 169–177.
Mathematical Reviews (MathSciNet): MR97b:58024
Zentralblatt MATH: 0865.57027
[6] R. Bott, On the Chern-Weil homomorphism and the continuous cohomology of Lie-groups, Advances in Math. 11 (1973), 289–303.
Mathematical Reviews (MathSciNet): MR49:9854
Zentralblatt MATH: 0276.55011
Digital Object Identifier: doi:10.1016/0001-8708(73)90012-1
[7] R. Bott, H. Shulman, and J. Stasheff, On the de Rham theory of certain classifying spaces, Advances in Math. 20 (1976), no. 1, 43–56.
Mathematical Reviews (MathSciNet): MR53:6583
Zentralblatt MATH: 0342.57016
Digital Object Identifier: doi:10.1016/0001-8708(76)90169-9
[8] R. Brown, Elements of Modern Topology, McGraw-Hill Book Co., New York, 1968.
Mathematical Reviews (MathSciNet): MR37:3563
Zentralblatt MATH: 0159.52201
[9] S. Eilenberg and S. MacLane, Relations between homology and homotopy groups of spaces, Ann. of Math. (2) 46 (1945), 480–509.
Mathematical Reviews (MathSciNet): MR7,137g
Zentralblatt MATH: 0061.40702
Digital Object Identifier: doi:10.2307/1969165
JSTOR: links.jstor.org
[10] V. V. Fock and A. A. Rosly, Flat connections and polyubles, Teoret. Mat. Fiz. 95 (1993), no. 2, 228–238.
Mathematical Reviews (MathSciNet): MR95a:58019
Zentralblatt MATH: 0849.58030
[11] W. M. Goldman, The symplectic nature of fundamental groups of surfaces, Adv. in Math. 54 (1984), no. 2, 200–225.
Mathematical Reviews (MathSciNet): MR86i:32042
Zentralblatt MATH: 0574.32032
Digital Object Identifier: doi:10.1016/0001-8708(84)90040-9
[12] K. Guruprasad, Flat connections, geometric invariants and the symplectic nature of the fundamental group of surfaces, Pacific J. Math. 162 (1994), no. 1, 45–55.
Mathematical Reviews (MathSciNet): MR94k:58022
Zentralblatt MATH: 0790.53029
Project Euclid: euclid.pjm/1102623045
[13] K. Guruprasad and C. S. Rajan, Group cohomology and the symplectic structure on the moduli space of representations, preprint, McGill Univ., 1995.
Mathematical Reviews (MathSciNet): MR1487982
Zentralblatt MATH: 0951.58016
Digital Object Identifier: doi:10.1215/S0012-7094-98-09107-4
Project Euclid: euclid.dmj/1077231892
[14] S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1978.
Mathematical Reviews (MathSciNet): MR80k:53081
Zentralblatt MATH: 0451.53038
[15] J. Huebschmann, Symplectic and Poisson structures of certain moduli spaces. I, Duke Math. J. 80 (1995), no. 3, 737–756.
Mathematical Reviews (MathSciNet): MR97f:58027
Zentralblatt MATH: 0852.58037
Digital Object Identifier: doi:10.1215/S0012-7094-95-08024-7
Project Euclid: euclid.dmj/1077246291
[16] J. Huebschmann, Symplectic and Poisson structures of certain moduli spaces. II. Projective representations of cocompact planar discrete groups, Duke Math. J. 80 (1995), no. 3, 757–770.
Mathematical Reviews (MathSciNet): MR97f:58028
Zentralblatt MATH: 0852.58038
Digital Object Identifier: doi:10.1215/S0012-7094-95-08025-9
Project Euclid: euclid.dmj/1077246292
[17] J. Huebschmann, The singularities of Yang-Mills connections for bundles on a surface. I. The local model, Math. Z. 220 (1995), no. 4, 595–609.
Mathematical Reviews (MathSciNet): MR97a:53033
Zentralblatt MATH: 0843.58009
Digital Object Identifier: doi:10.1007/BF02572633
[18] J. Huebschmann, The singularities of Yang-Mills connections for bundles on a surface. II. The stratification, Math. Z. 221 (1996), no. 1, 83–92.
Mathematical Reviews (MathSciNet): MR97a:53034
Zentralblatt MATH: 0844.58011
Digital Object Identifier: doi:10.1007/BF02622101
[19] J. Huebschmann, Smooth structures on moduli spaces of central Yang-Mills connections for bundles on a surface, to appear in J. Pure Appl. Alg.; dg-ga/9411008.
[20] J. Huebschmann, Poisson structures on certain moduli spaces for bundles on a surface, Ann. Inst. Fourier (Grenoble) 45 (1995), no. 1, 65–91.
Mathematical Reviews (MathSciNet): MR96a:58038
Zentralblatt MATH: 0819.58010
[21] J. Huebschmann, Poisson geometry of flat connections for $\rm SU(2)$-bundles on surfaces, Math. Z. 221 (1996), no. 2, 243–259.
Mathematical Reviews (MathSciNet): MR97f:58029
Zentralblatt MATH: 0844.58014
[22] J. Huebschmann, Poisson geometry of certain moduli spaces, Rend. Circ. Mat. Palermo (2) Suppl. (1996), no. 39, 15–35, The Proceedings of the Winter School “Geometry and Physics” (Srni, 1994).
Mathematical Reviews (MathSciNet): MR97h:58030
Zentralblatt MATH: 00896246
[23] J. Huebschmann and L. Jeffrey, Group cohomology construction of symplectic forms on certain moduli spaces, Internat. Math. Res. Notices (1994), no. 6, 245 ff., approx. 5 pp. (electronic).
Mathematical Reviews (MathSciNet): MR95e:58033
Zentralblatt MATH: 0816.58017
[24] L. Jeffrey, Extended moduli spaces of flat connections on Riemann surfaces, Math. Ann. 298 (1994), no. 4, 667–692.
Mathematical Reviews (MathSciNet): MR95g:58030
Zentralblatt MATH: 0794.53017
Digital Object Identifier: doi:10.1007/BF01459756
[25] L. Jeffrey, Symplectic forms on moduli spaces of flat connections on $2$-manifolds, Geometric topology (Athens, GA, 1993) ed. W. Kazez, AMS/IP Stud. Adv. Math., vol. 2, Amer. Math. Soc., Providence, RI, 1997, Georgia International Topology Conference, pp. 268–281.
Mathematical Reviews (MathSciNet): MR99b:58043
Zentralblatt MATH: 0904.57009
[26] L. Jeffrey, Group cohomology construction of the cohomology of moduli spaces of flat connections on $2$-manifolds, Duke Math. J. 77 (1995), no. 2, 407–429.
Mathematical Reviews (MathSciNet): MR96m:58029
Zentralblatt MATH: 0870.57013
Digital Object Identifier: doi:10.1215/S0012-7094-95-07712-6
Project Euclid: euclid.dmj/1077286347
[27] Y. Karshon, An algebraic proof for the symplectic structure of moduli space, Proc. Amer. Math. Soc. 116 (1992), no. 3, 591–605.
Mathematical Reviews (MathSciNet): MR93a:14010
Zentralblatt MATH: 0790.14012
Digital Object Identifier: doi:10.2307/2159424
JSTOR: links.jstor.org
[28] S. MacLane, Homology, Die Grundlehren der mathematischen Wissenschaften, Bd. 114, Academic Press Inc., Publishers, New York, 1963.
Mathematical Reviews (MathSciNet): MR28:122
Zentralblatt MATH: 0133.26502
[29] M. S. Narasimhan and C. S. Seshadri, Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math. (2) 82 (1965), 540–567.
Mathematical Reviews (MathSciNet): MR32:1725
Zentralblatt MATH: 0171.04803
Digital Object Identifier: doi:10.2307/1970710
JSTOR: links.jstor.org
[30] H. B. Shulman, Characteristic classes and foliations, Ph.D. thesis, University of California, 1972.
[31] R. Sjamaar and E. Lerman, Stratified symplectic spaces and reduction, Ann. of Math. (2) 134 (1991), no. 2, 375–422.
Mathematical Reviews (MathSciNet): MR92g:58036
Zentralblatt MATH: 0759.58019
Digital Object Identifier: doi:10.2307/2944350
JSTOR: links.jstor.org
[32] H. F. Trotter, Homology of group systems with applications to knot theory, Ann. of Math. (2) 76 (1962), 464–498.
Mathematical Reviews (MathSciNet): MR26:761
Zentralblatt MATH: 0108.18302
Digital Object Identifier: doi:10.2307/1970369
JSTOR: links.jstor.org
[33] A. Weil, Remarks on the cohomology of groups, Ann. of Math. (2) 80 (1964), 149–157.
Mathematical Reviews (MathSciNet): MR30:199
Zentralblatt MATH: 0192.12802
Digital Object Identifier: doi:10.2307/1970495
JSTOR: links.jstor.org
[34] A. Weinstein, The symplectic structure on moduli space, The Floer memorial volume ed. H. Hofer, et al., Progr. Math., vol. 133, Birkhäuser, Basel, 1995, pp. 627–635.
Mathematical Reviews (MathSciNet): MR97g:58031
Zentralblatt MATH: 0834.58011
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